A square is incribed in an isoceles right triangle, so that the square and the triangle have one angle common. Show that the vertex of the sqare opposite the vertex of the common angle bisects the hypotenuse.

Explanation

To solve the problem, we need to show that the vertex of the square opposite the common angle bisects the hypotenuse of the isosceles right triangle. Here’s a step-by-step solution:

### Step 1: Draw the Isosceles Right Triangle
- Let triangle ABC be an isosceles right triangle where \( AB = AC \) and \( \angle A = 90^\circ \). The hypotenuse is \( BC \).

### Step 2: Inscribe the Square
- Inscribe a square \( BDEF \) in triangle ABC such that one angle of the square (angle \( B \)) is at point B, and the square touches side AC at point D and side AB at point E.

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